Optics Laws of lenses and optical instruments. Geometrical Optics. What you need:

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1 Optics Geometrical Optics..0 Laws of lenses and optical instruments What you can learn about Law of lens es Mag nifi ca tion Focal length Object dis tance Tele scope Micro scope Path of a ray Con vex lens Con cave lens Real image Vir tu al image Principle: The focal lengths of unknown lens es are deter mined by meas ur ing the dis tanc es of image and object and by Bessel s meth od. Simple opti cal instru ments are then con struct ed with these lens es. What you need: Lens, mounted, f = +0 mm Lens, mounted, f = +50 mm Lens, mounted, f = +00 mm Lens, mounted, f = +300 mm Lens, mounted, f = -50 mm Lens, mounted, f = -00 mm Screen, translucent, 50 mm x 50 mm Screen with arrow slit Ground glass screen, 50 mm d = 50 mm Double condenser, f = 60 mm Object micrometer mm i.00 parts 67.9 Ctenocephalus, msl Slide -Emperor Maximilian Optical profile bench, l = 000 mm Base for optical profile bench, adjustable Slide mount for optical profil bench, h = 30 mm Slide mount for optical profil bench, h = 80 mm Diaphragm holder for optical base plate Lens holder Condenser holder Swinging arm Experimenting lamp 5, with stem 60.0 Power supply 0- V DC/ 6 V, V AC Connecting cable, 4 mm plug, 3 A, blue, l = 50 cm Rule, plastic, 00 mm Complete Equipment Set, Manual on CD-ROM included Laws of lenses and optical instruments P000 Path of a ray in Galileo tele scope. Tasks:. To deter mine the focal length of two unknown con vex lens es by meas ur ing the dis tanc es of image and object.. To deter mine the focal length of a con vex lens and of a com bi na tion of a con vex and a con cave lens using Bessel s meth od. 3. To con struct the fol low ing opti cal instru ments:. Slide pro jec tor; image scale to be deter mined. Microscope; mag nifi ca tion to be deter mined 3. Kepler-type tele scope 4. Galileo s tele scope (opera glass es). 90 Laboratory Experiments Physics PHYWE Systeme GmbH & Co. KG D Göttingen

2 Laws of lenses and optical instruments LEP..0 Related topics Law of lenses, magnification, focal length, object distance, telescope, microscope, path of a ray, convex lens, concave lens, real image, virtual image. Principle The focal lengths of unknown lenses are determined by measuring the distances of image and object and by Bessel s method. Simple optical instruments are then constructed with these lenses. Equipment Lens, mounted, f = +0 mm Lens, mounted, f = +50 mm Lens, mounted, f = +00 mm Lens, mounted, f = +300 mm Lens, mounted, f = 50 mm Lens, mounted, f = 00 mm Screen, translucent, mm Screen, with arrow slit Ground glass screen, mm Double condenser, f = 60 mm Stage micrometer, mm - 00 div Dog flea, Ctenocephalus, mip Slide -Emperor Maximilian Optical profile-bench, l = 000 mm Base f. opt.profile-bench, adjust Slide mount f. opt.pr.-bench, h = 30 mm Slide mount f. opt.pr.-bench, h = 80 mm Diaphragm holder Lens holder Condenser holder Swinging arm Experiment lamp 5, with stem 60.0 Power supply 0- V DC/6 V, V AC Connecting cord, l = 500 mm, blue Rule, plastic, l = 00 mm Tasks. To determine the focal length of two unknown convex lenses by measuring the distances of image and object.. To determine the focal length of a convex lens and of a combination of a convex and a concave lens using Bessel s method. 3. To construct the following optical instruments:. Slide projector; image scale to be determined. Microscope; magnification to be determined 3. Kepler-type telescope 4. Galileo s telescope (opera glasses). Set-up and procedure The experiment is set up as shown in Fig.. A parallel light beam is produced with the lamp and the double condenser.. The object (screen with arrow slit) is directly behind the condenser, and a clear image is projected on to the screen with a lens. The distances of image and object from the lens are measured (assume that the lenses are thin). Fig. : Experimental set-up (microscope). PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen P000

3 LEP..0 Laws of lenses and optical instruments The measurement of distances of image and object is repeated, using both lenses and with the lens and the screen in different positions.. If, at a fixed distance d between object and image (case ), we alter the position of the lens so that the image and object distances are transposed (case ), we still obtain a clear image of the object. In case the image is magnified, in case it is reduced (Fig. ). 3. Microscope A magnifield image of a small object (stage micrometer and micro-slide of a dog flea) is produced with a lens L of short focal length f = +0 mm. The real intermediate image is observed through an eyepiece L (f = +50 mm) (Fig. 4). The ground glass and the object holder with the object are fixed in the swinging arm. L is brought as close to the object as possible. The object is illuminated through a ground glass screen. The size of the image and thence the overall magnification are roughly determined by comparing it with a scale at the least distance of distinct vision (approximately 5 cm). To do this we look through the microscope with the right eye and at the scale with the left. With practice the two images can be superimposed. Fig. : Determination of focal length after Bessel. Using a convex lens of focal length +00 mm, for instance, measure the distance e at which a sharp image is obtained for both possible lens positions (repeat the measurement and calculate the average value e. Now take a measurement in the same way but using the convex lens from the first measurement and a concave lens (-00 mm for example). Make the distance d as large as possible, and measure at least four times the combined forcal length. 3.. Slide projector Place the slide Emperor Maximilian immediately behind the condenser and project an image on the screen with the lens L (f = +00 mm). Fig. 4: Path of a ray in the microscope. 3.3 Telescope after Kepler A convex lens of long focal length f (+300 mm, for example), and one of short focal length f (e.g. +50 mm) are secured to the optical bench at a distance of f + f (Fig. 5). To obtain the best image illumination set the condenser so that the image of the lamp coil is in the plane of objective lens L (Fig. 3). Determine the magnification V of the image V B G Fig. 5: Path of a ray in a Kepler telescope. If we look through the lens of short focal length, we can see an inverted, magnified image of a distant object. 3.4 Galileo telescope (opera glasses) A convex lens of long focal length ƒ (+300 mm, for example) and a concave lens of short focal length f (e.g. -50 mm) are set up at a distance of f f - (Fig. 6). Fig. 3: Path of a ray in a slide projector. Through the concave lens we can see distant object magnified and the right way up. P000 PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen

4 Laws of lenses and optical instruments LEP..0 The focal length of the convex lens can therefore be determined from the measured values of d and e. Fig. 6: Path of a ray in Galileo telescope. Theory and evaluation The relationship between the focal length f of a lens, the object distance g and the image distance b is obtained from geometrical optics. Three particular rays, the focal ray, the parallel ray and the central ray, are used to construct the image (Fig. 7). Fig. 7: Image construction with three principal rays. From the laws of similar triangles, B G b g where B is the image size and G is the object size. By transforming we obtain the lens formula ƒ b g. From the values of b and g measured in Task we calculate f, the average value of f and its standard deviation. For the first lens (00 mm) f was 00. mm with a standard deviation s f of 0.6 mm; for the second (50 mm), f was 53. mm with a standard deviation s f of 0.9 mm. (The focal lengths marked on the lenses have a tolerance of ±5%.). Since g = b (the object distance in case = image distance in case ) and since b = g, g + b = d g - b = e (see Fig. ). If we solve the equations for g and b we obtain g = (d + e) b = (d e) Substituting into the lens formula gives f = d e 4d and G B ƒ b ƒ b g or ƒ b g If we now use a lens system of focal length f comb. consisting of the convex lens already measured (focal length f s ) and a concave lens, and carry out the measurement in the same way, we obtain the following for the focal length of the concave lens f z : ƒ z ƒ comb. ƒ s or ƒ z ƒ comb. ƒ s ƒ s ƒ comb. Here we assume that 0 f s 0 as otherwise no real images would be produced. f was 99.7 mm for the convex lens (+00 mm), f comb. was 80 mm for the combination of two lenses (+00 mm/-00 mm) so that f z = -3 mm represents the focal length of the concave lens. (The combination of two lenses involves a systematic error as the distance between the principal planes is disregarded). 3. The magnification is obtained from the relationship between object size and image size b V B G b f f When the image distance b is 700 mm and the focal length f =00 mm, then V = The overall magnification is obtained by multiplying the magnification due to the objective (Fig. 4), b objective Y a a Y g f by the angular magnification of the eyepice 50 mm L f With the lenses used we obtain an overall magnification V = The objective L provides a real, inverted image of size Y of a very distant object, and this image is observed through the eyepiece L. The angular magnification (for small angles) is L = > 0 f z 0 e e Y >f f Y >f f 3.4 A concave lens is placed in the path of the ray in front of the real first image produced by objective L so that the focal points F and F coincide. The eye then sees a virtual, upright image. The magnification is once again f L = 0 f 0 Note The markings on the lenses used to measure focal length should be removed and replaced by a code, e.g. coloured dots or etched lines, known only to the instructor. PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen P000 3

5 LEP..0 Laws of lenses and optical instruments 4 P000 PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen